Question

A Swedish tour guide has devised a clever way for his clients to recognize him. He owns 13 pairs of shoes of the same style, customized so that each pair has a unique color. How many ways are there for him to choose a left shoe and a right shoe from these 13 pairs?

Answer 1

The number of ways for a Swedish tour guide to choose a left shoe and a right shoe from 13 uniquely colored pairs is 169, by multiplying the number of choices for each shoe (13 for left and 13 for right).

Step-by-step explanation:

The student is asking about a combinatorial mathematics problem concerning selecting shoes with unique colors. Given that there are 13 pairs of shoes, each with a unique color, the number of ways to select a left shoe is 13, and similarly, the number of ways to select a right shoe is also 13.

However, since the selection of a left shoe is independent of the selection of a right shoe, these two choices can be made in a combinatorial manner. To calculate the total number of combinations possible, we simply multiply the number of options for the left shoe by the number of options for the right shoe (assuming the tour guide does not mind wearing mismatched shoes). Therefore, the number of combinations is 13 (for the left shoe) times 13 (for the right shoe), which equals 169 possible combinations.

Answer 2

P(13,2) = 169

Step-by-step explanation:

We have to calculate the combinations for left and right shoe considering is not the same having a right shoe blue and left red than having a right shoe rend and a left red.

there are 13 pairs from whcih she will take a single pair:

`P(n,r) = n^(r) \\`

where:

n = number of pair = 13

r = shoes = 2 (one on each foot)

`P(n,r) = 13^(2) \\`

P(13,2) = 169